4. The R() relation of [M/H] ZAMS dwarfs
For stars of given age and metallicity, theory provides the radius as a function of absolute magnitude, e.g. . In the present context this follows from the fact that the models yield as a function of which transforms Eq. (6) into () and Eq. (2) into R().
Fig. 3a shows the observed radii of YY Gem (mean component) and the eight YD, four old disk (OD), and four halo (H) M-dwarfs of L96 along with the BCAH98 model radii for solar-composition ZAMS stars (solid curve, see also Fig. 1 of Paper I). There is no obvious difference between the radii of YD and OD stars in this rather restricted sample. The two faint H stars show the expected smaller radii. This is consistent with the small metallicity dependence of the R() BCAH98 models which can approximately be expressed by log per 1 dex reduction of [M/H] relative to solar (BCAH98). On the average, the L96 radii of the YD/OD stars exceed the [M/H] = 0 ZAMS model radii by 2% (Paper I) which is within the systematic uncertainties of the L96 radii. These model radii (solid curve) can be represented reasonably well by a third-order polynomial in which we adjust slightly, by , to nominally fit the L96 radii (dot-dashed curve in Fig. 3a)
We accept Eq. (7) as representative of ZAMS stars with near-solar or slightly reduced metallicities (kinematic classes YD and OD). Note that radii for stars fainter than are still uncertain because dust formation is not accounted for in the BCAH98 models
Stellar radii may be estimated either from a Barnes-Evans type relation as Eq. (6) together with Eq. (2) or directly from the R() relation in Eq. (7). The former depends weakly on gravity but distinctly on metallicity, while the latter depends weakly on metallicity and strongly on gravity and, therefore, requires knowledge of the evolutionary status.
The different metallicity dependencies of the two approaches arise because reference is taken to a colour in one case and directly to the abolute magnitude in the other. The difference in the approaches becomes more obvious when combining Eqs. (2), (6), and (7) to yield the colour-magnitude relation vs. for ZAMS stars of near-solar metallicity
(Fig. 3b, dot-dashed curve). Eq. (8) closely fits the L96 YD stars (encircled dots) which is as expected because Eqs. (6) and (7) fit these stars, too. Although Eq. (7) is approximately valid also for OD stars with slightly reduced metallicity, Eq. (6) and Eq. (8) are not. At the same , stars of lower metallicity (open points, triangles in Fig. 3b) are bluer. They have nearly unchanged and radii, however, because the metallicity dependence of the colour in Fig. 3b and the metallicity dependence of in Fig. 2b compensate approximately. This implies that application of the Barnes-Evans relations in Fig. 2 requires knowledge of the metallicity of the respective stars.
© European Southern Observatory (ESO) 1999
Online publication: July 26, 1999